POD-LSTM based rapid prediction of water-exit forces on a NACA 4412 hydrofoil

To overcome the low efficiency and high computational cost of conventional CFD simulations for water-exit problems, this paper develops a fast prediction method combining Proper Orthogonal Decomposition (POD) and Long Short-Term Memory (LSTM) neural networks. The entire water-exit process is divided into five typical stages according to the evolution of vertical force coefficients. POD analysis identifies dominant flow structures from static pressure fields for each stage. Parametric studies reveal that exit velocity primarily adjusts the flow evolution timescale without altering intrinsic flow features, whereas the angle of attack strongly affects the spatiotemporal flow characteristics. A dual-module prediction framework is then constructed, consisting of a force coefficient predictor and a POD temporal coefficient predictor. Numerical validation demonstrates that the first ten POD modes well capture transient flow features, achieving a determination coefficient R 2 > 0.994 for force coefficient prediction. Using only ten initial time steps of POD coefficients, the full-sequence temporal coefficients are predicted with R 2 > 0.995. The integrated model requires merely operating parameters and limited initial flow data, and its predictions agree well with CFD results. This method greatly cuts computational cost and serves as an accurate and efficient tool for multi-condition performance evaluation of cross-medium vehicles.